export IPTC location information

Make sure that in the Export window, Remove Location Info is unchecked:

If that doesn't help: How are you examining the IPTC metadata after export?

In the Map module, do you have any Saved Locations?  If so, check each one to make sure they're not marked as Private.

No need to use the Map module to get IPTC location information recorded properly. 

Nevertheless, check the Map module's Saved Locations as described above to make sure there is no saved location marked as Private that's blocking the export of location information.

If your Map module has no saved locations then: In Library mode, select one of the problematic pics. In the Metadata panel, select the Location preset.  Make a screenshot of the entire LR window and post it here.  Then export that pic, upload it to Dropbox or similar, and post the link here.   That should provide enough clues as to what's going on.

When I export then open in Photoshop to look at file info the description panel is fully written (author, description, keywords, copyright) but the IPTC extension panel is completely blank

Ah, in Photoshop the IPTC City, State/Province, and Country fields are in the Origin section:

In Bridge, they're in the IPTC Core section:

Why does NOTHING populate the IPTC extension panel? 

The fields from LR's Metadata > IPTC Extension panel populate the fields that show up under Photoshop and Bridge's IPTC Extension panels.   Though they have some labels in common, the Extension and Core fields are in fact completely separate groups of fields.

How do you get fields to populate in the main panel instead?

I can't help much on that.  I believe you can customize the metadata panels in both Photoshop and Bridge (e.g. see this thread), but it looks fairly involved and only partially documented.